Capacity achieving two-write WOM codes

Authors:
Amir Shpilka
Affiliations:
Faculty of Computer Science, Technion -- Israel Institute of Technology, Haifa, Israel
Venue:
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Year:
2012

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Abstract

In this paper we give several new constructions of WOM codes. The novelty in our constructions is the use of the so called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction of a two-write Write-Once-Memory (WOM for short) code that approaches capacity, over the binary alphabet. More formally, for every ε0, 0pn=(1/ε)O(1/pε) we give a construction of a two-write WOM code of length n and capacity H(p)+1−p−ε. Since the capacity of a two-write WOM code is max p (H(p)+1−p), we get a code that is ε-close to capacity. Furthermore, encoding and decoding can be done in time O(n2·poly(logn)) and time O(n·poly(logn)), respectively, and in logarithmic space. We highlight a connection to linear seeded extractors for bit-fixing sources. In particular we show that obtaining such an extractor with seed length O(logn) can lead to improved parameters for 2-write WOM codes.